The Dublin North West TD does not intend to call a snap election and would not appoint a Brexit minister if he succeeds in the Fine Gael leadership race.
Mr Varadkar, due to publish his policy proposals today, said the campaign is going “very well” but added that he is happy that rival Simon Coveney has remained in the contest.
“I am very keen as well that the contest should continue and I am pleased that Simon Coveney has decided to stay in the contest because it’s absolutely important that we take this debate and this opportunity to reinvigorate Fine Gael to the councillors and the members across the country,” said the Social Protection Minister.
Mr Varadkar has already gained the support of 45 Fine Gael TDs, senators and MEPs, while Mr Coveney has the public backing of 20.
In the policy document is a promise of an “extensive investment programme” in national cultural institutions, with priority given to enhance arts in education.
Mr Varadkar also hopes to grow Ireland’s audio visual sector with a strategy to attract more international productions, and resource greater domestic output.
Bursaries to support emerging sportspeople and artists would also be made available.
Speaking before taking part in a 5k run around Dublin’s docklands area, Mr Varadkar said he had thought about a Brexit minister, but the only country to create such a position is Britain, which is leaving the EU.
“Every single European meeting that happens is a meeting of counterparts, a meeting of equals,” he said.
“The big decisions are made at the European Council, which the prime ministers attend, so if we had a Brexit minister, the Brexit minister wouldn’t be able to attend meetings where decisions are made.
“The second level of decision-making is made at the general affairs council and that’s where the European affairs ministers attend, so the Brexit minister wouldn’t even be able to attend the second-most important meeting about Brexit.”